惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

V
V2EX
人人都是产品经理
人人都是产品经理
WordPress大学
WordPress大学
博客园 - Franky
小众软件
小众软件
酷 壳 – CoolShell
酷 壳 – CoolShell
Apple Machine Learning Research
Apple Machine Learning Research
爱范儿
爱范儿
IT之家
IT之家
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
V
Visual Studio Blog
S
SegmentFault 最新的问题
美团技术团队
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
有赞技术团队
有赞技术团队
B
Blog RSS Feed
Last Week in AI
Last Week in AI
Jina AI
Jina AI
博客园 - 司徒正美
The Cloudflare Blog
博客园_首页
博客园 - 聂微东
宝玉的分享
宝玉的分享
大猫的无限游戏
大猫的无限游戏

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees
Picard-Lefschetz theory and alien calculus: a case study
[Submitted on 9 May 2026 (v1), last revised 25 Jun 2026 (this ve · 2026-06-26 · via math updates on arXiv.org

View PDF

Abstract:We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefschetz side, we describe the Lefschetz thimbles and compute the connecting trajectories between critical points appearing at Stokes phases. On the resurgent side, we analyze the Borel singularities of the saddle expansions and use alien operators to recover the same Stokes coefficients. These examples serve as explicit finite-dimensional test cases for the dictionary between thimble wall-crossing and alien calculus.

Submission history

From: Si Li [view email]
[v1] Sat, 9 May 2026 10:39:35 UTC (43 KB)
[v2] Thu, 25 Jun 2026 03:54:10 UTC (46 KB)